This text describes ancient calendar calculation methods, which are quite professional and complex. Let's explain it in modern language, sentence by sentence.
First, "The lunar calendar has four tables, three trajectories, intersecting and dividing the celestial sphere, dividing by the lunar rate to obtain the days of the calendar." This means: based on the four tables of the moon's movement (possibly referring to different observational data), as well as the three trajectories of the moon's movement (possibly referring to different calculation methods), combining them and calculating according to the speed of the moon's movement, you can obtain the date of each day. This part explains the basics of calendar calculation.
Next, "Multiply the lunar cycles and the new moons together, like a conjunction of the new moons. Multiply the common factors by the meeting factor; the remainder is like the meeting factor, the retreat is the separation. Proceed with the month, for the daily progress. The meeting factor is one, the difference rate is also." These sentences are more abstract. "Weeks" refer to a year, "weeks and new moons together" refer to the cycle from new moon to full moon and back to new moon, "meeting of the months" may refer to a specific point in time. In general, this passage describes a calculation method, through some multiplication and division operations, to obtain a "difference rate" for subsequent calculations. This part is the core step of the calculation method.
Then there is the table section, which lists the "gain and loss ratio" and "joint number" for each day. This part involves specific numerical calculations, which are difficult to directly translate into modern language because they depend on specific parameters and calculation methods of ancient calendars. In simple terms, every day is adjusted based on specific rules to more accurately reflect the moon's movement. For example, "on the first day, reduce by one day and increase by seventeen units" means reducing one day on the first day and adding seventeen of some unit (unit not specified). The following "second day," "third day," and so on, all follow similar adjustment rules. The meaning of these numbers needs to be understood in conjunction with the knowledge of ancient calendars at that time, which will not be explained here.
"At the limit, a remainder of three thousand nine hundred twelve, with a correction factor of one thousand seven hundred fifty-two. This is referred to as the later limit." This sentence means: after calculating to a certain stage, a remainder of three thousand nine hundred twelve is obtained, along with a correction factor of one thousand seven hundred fifty-two, and this stage is referred to as the "later limit." This part is a record of the calculation results.
"The method for determining the final result involves taking the month of the conjunction and adding it to the month of the full moon phase, then multiplying the remaining new moon and its fractional parts by each other. The fractional part is adjusted according to the method derived from the new moon, and the full moon phase is subtracted from the complete cycle, leaving the remainder that does not complete the cycle is entered into the solar calendar; the remainder is then entered into the lunar calendar. The remainder, calculated as one day for each lunar cycle, is sought to determine the new moon's entry into the calendar, which does not completely account for the extra days." This passage describes the final step in calendar calculation. Through a series of computations, it ultimately determines whether the day belongs to the solar or lunar calendar and calculates the remaining date. This part is the final step of the calendar calculation and is also the most difficult to understand.
Finally, by adding two days, the total remaining days becomes two thousand five hundred eighty, with a fractional part of nine hundred fourteen. Using the method, this forms a day; subtracting thirteen gives a remainder that is divided as fractional days. The solar and lunar calendars interweave, with the entry into the calendar occurring before the remainder reaches the limit, and the remainder after the limit being the midpoint of the lunar cycle. Each is placed into the slow and fast calendars, with the full and reduced cycles calculated; the total days multiplied by the small fractions form the fractional parts, with the increase and decrease adjusting the solar and lunar days. The excess days are adjusted by either advancing or retreating the days. The remaining days are defined by multiplying the gain and loss rate, as one day corresponds to each lunar cycle, with the gain and loss combined to define the time.
In summary, this text describes a very complex ancient calendar calculation method, with underlying mathematical principles and astronomical observation knowledge that are quite profound. Explaining it in modern vernacular is relatively difficult and requires an in-depth understanding of ancient calendars for complete comprehension.
First, multiplying the difference rate by the decimal part of the remaining new moon day, similar to calculus, yields a numerical value, which is then subtracted from the remaining days calculated in the calendar. If it is insufficient to subtract, a full month’s cycle is added before subtracting, and then one day is retreated. The resulting remaining days are then added to their fractional part, simplifying the small fractions to obtain the moment when the new moon phase is recorded in the calendar at midnight.
Next, to find the next day, add one day; the remaining days total 31, and the small fraction is also 31. If the small fraction exceeds the total number of days, subtract a full month’s cycle. Then add one more day; the calendar calculation continues until the end. If the remaining days exceed the fractional days, subtract the fractional days, which gives the starting moment of entry into the calendar. If the remaining days do not complete the fractional days, keep them, adding 2720, with the small fraction being 31, thereby determining the moment of transition into the next calendar."
Using the total number multiplied by the lunar phases of fullness and contraction in the calendar, as well as the remaining days, if the remaining days exceed half a week, it is considered a subdivision. Adding the full number to the contraction value, then subtracting the Yin and Yang residual days, if there is either a surplus or a deficiency in the residual days, adjust the days using the lunar month and the solar week. Multiply the established residual days by the profit and loss rate; if it equals the lunar month and solar week, use the overall profit and loss value as the established value for midnight.
Multiply the profit and loss rate by the time of the nearest solar term at night, divide by 200 to determine the sunrise time, subtract this value from the profit and loss rate to determine the sunset time, and use the profit and loss midnight number as the established value for sunrise and sunset.
If adding the time equals the established value for sunrise and sunset, divide by 12 to get the degree; one-third of the remainder indicates a deficiency, less than one minute indicates strength, and two deficiencies indicate weakness. The resulting value is the angle of the moon's deviation from the ecliptic. For the solar calendar, subtract the extreme from the ecliptic position of the day; for the lunar calendar, add the extreme to the ecliptic position of the day to get the degree of the moon leaving the extreme. Positive for strength, negative for weakness, combine the strengths and weaknesses, subtract items of the same type and add items of different types. When subtracting, subtract items of the same type, add items of different types; if there is no complement, add two strengths and subtract one weakness.
Beginning from the Ji-Chou year of the Yuan Dynasty to the Bing-Xu year in the eleventh year of Jian'an, a total of 7378 years:
- Ji-Chou
- Wu-Yin
- Ding-Mao
- Bing-Chen
- Yi-Si
- Jia-Wu
- Gui-Wei
- Ren-Shen
- Xin-You
- Geng-Xu
- Ji-Hai
- Wu-Zi
- Ding-Chou
- Bing-Yin
The Five Elements: Wood (Jupiter), Fire (Mars), Earth (Saturn), Metal (Venus), and Water (Mercury). Use their respective end days and celestial degrees to obtain the weekly rate and daily rate. Multiply the chapter by the weekly rate to obtain the monthly method. Multiply the chapter by the monthly method to obtain the monthly division. Divide the monthly division by the monthly method to get the month number. Multiply the total number by the monthly method to get the daily method. Multiply the Dipper by the weekly rate to get the Dipper. (The daily method uses the record method multiplied by the weekly rate, so here we also use division to multiply.)
The large and small remainders of the five stars on the first day of the lunar month. (Multiply the total method by the month number separately, divide by the daily method separately, get the large remainder, and the remainder that cannot be divided is the small remainder. Subtract the large remainder from 60.)
The five stars enter the month and the daily remainder. (Multiply the total method by the month remainder separately, multiply the combined month method by the first day of the month small remainder, add the two, simplify with the total, divide by the daily method, and you will get the results.)
This passage records some data calculated by ancient astronomical calendars; let's break it down sentence by sentence in contemporary language.
First, "the degrees and remaining degrees of the five stars. (Subtract the integer part for the remaining degree part, multiply by the number of weeks, and approximate using the daily degree method; the result gives the degree, while the remainder indicates the remaining degree. If it exceeds the number of weeks, subtract the weeks and add the 斗分.)" This sentence means to calculate the degrees and remaining degrees of the five stars. The calculation method is: first subtract the integer part, what remains is the remaining degree part, then multiply the remaining degree part by the number of weeks, and divide by the daily degree method; the quotient gives the degree, while the remainder indicates the remaining degree. If the remaining degree exceeds the number of weeks, subtract the weeks and add the 斗分. In short, this is a complex astronomical calculation method that involves many astronomical units.
Next, "the month count totals seven thousand two hundred eighty-five; the leap month count is seven; the month total is two hundred thirty-five; there are twelve in a year; the total method is forty-three thousand twenty-six; the daily method is one thousand four hundred fifty-seven; the meeting number is forty-seven; the number of weeks is two hundred fifteen thousand one hundred thirty; the 斗分 is one hundred forty-five." These are some basic parameters in astronomical calendars, such as how many months are in a year (month count), how many leap months there are (leap month count), etc. These numbers represent different astronomical cycles and units, serving as the basis for subsequent calculations.
"Jupiter: the weekly rate totals six thousand seven hundred twenty-two; the daily rate is seven thousand three hundred forty-one; the total month count is thirteen; the remaining month count is sixty-four thousand eight hundred one; the total month method is one hundred twenty-seven thousand seven hundred eighteen; the daily degree method is three million nine hundred fifty-nine thousand two hundred fifty-eight; the large new moon remainder is twenty-three; the small new moon remainder is one thousand three hundred seven; the day of entry into the new month is fifteen; the daily remainder is three million four hundred eighty-four thousand six hundred forty-six; the new moon 虚分 is one hundred fifty; the 斗分 is nine hundred seventy-four thousand six hundred ninety; the degree is thirty-three; the remaining degree is two million nine hundred ninety-nine thousand five hundred fifty-six." This section is about specific data for Jupiter, including its weekly rate, daily rate, etc. These data are related to Jupiter's orbital period and position, used for more accurate calculations of Jupiter's trajectory. Behind these numbers are complex calculations; we only need to understand that these represent specific parameters of Jupiter's movement.
"Fire: Orbital circumference, three thousand four hundred seventy; orbital daily rate, seven thousand two hundred seventy-one; total lunar cycles, twenty-six; remaining lunar months, twenty-five thousand six hundred twenty-seven; combined lunar calculation method, sixty-four thousand seven hundred thirty-three; daily degree calculation method, two million six thousand seven hundred twenty-three; large new moon excess, forty-seven; small new moon excess, one thousand one hundred fifty-seven; day of entry into the lunar month, twelve; remaining days, nine hundred seventy-three thousand one hundred thirteen; virtual division of the new moon, three hundred; 斗分, four hundred ninety-four thousand one hundred fifteen; number of degrees, forty-eight; remaining degrees, one hundred ninety-nine million one thousand seven hundred six." This section is about Mars, similar data describing the parameters of Mars' trajectory.
"Earth: Orbital circumference, three thousand five hundred twenty-nine; orbital daily rate, three thousand six hundred fifty-three; total lunar cycles, twelve; remaining lunar months, fifty-three thousand eight hundred forty-three; combined lunar calculation method, sixty-seven thousand fifty-one; daily degree calculation method, two hundred seventy-eight thousand five hundred eighty-one; large new moon excess, fifty-four; small new moon excess, five hundred thirty-four; day of entry into the lunar month, twenty-four; remaining days, one hundred sixty-six thousand two hundred seventy-two; virtual division of the new moon, nine hundred twenty-three; 斗分, five hundred eleven thousand seven hundred five; number of degrees, twelve; remaining degrees, one hundred seventy-three thousand three hundred forty-eight." This section contains the calculation data for Saturn, similar to the previous data for Jupiter and Mars.
"Metal: Orbital circumference, nine thousand twenty-two; orbital daily rate, seven thousand two hundred thirteen; total lunar cycles, nine." Finally, this is the data for Venus, with only part of the parameters listed. These data were derived by ancient astronomers through long-term observation and complex calculations, reflecting the exquisite level of ancient astronomical calendars. Although we now find it difficult to understand the specific processes of these calculations, these numbers themselves record the achievements of ancient astronomical research.
A month has passed, and the value is one hundred fifty-two thousand two hundred ninety-three.
According to the combined lunar calculation method, the result is one hundred seventy-one thousand four hundred eighteen.
Using the daily degree calculation method, the result is five hundred thirty-one thousand three hundred ninety-eight.
The large new moon excess is twenty-five.
The small new moon excess is one thousand one hundred twenty-nine.
The day of entry into the lunar month is twenty-seven.
The remaining days are fifty-six thousand nine hundred fifty-four.
The virtual division of the new moon is three hundred twenty-eight.
斗分 is one hundred thirty thousand eight hundred ninety.
The number of degrees is two hundred ninety-two.
The remaining degrees are fifty-six thousand nine hundred fifty-four.
The circumference of water (水) is eleven thousand five hundred and sixty-one. The circumference of the sun (日) is one thousand eight hundred and thirty-four. The total number of months is one (合月数是一). Next, after one month, the value is two hundred and eleven thousand three hundred and thirty-one (数值是二十一万一千三百三十一). According to the combined month method (合月法), the result is two hundred and nineteen thousand six hundred and fifty-nine. Using the daily method (日度法), the result is six hundred and eighty thousand nine hundred and forty-nine (六百八十万九千四百二十九). The large remainder of the new moon (朔大余) is twenty-nine. The small remainder of the new moon (朔小余) is seven hundred and seventy-three. The day of entering the month (入月日) is twenty-eight. The day's remainder (日余) is six hundred and forty-one thousand nine hundred and sixty-seven. The moon's virtual fraction is six hundred and eighty-four. The Dipper fraction is one hundred and sixty-seven thousand six hundred and forty-five. The degree is fifty-seven. The degree's remainder is six hundred and forty-one thousand nine hundred and sixty-seven.
Okay, next is the calculation method: first, multiply the total number of years by the circumference; if it can be evenly divided by the daily rate to get one, it is called the integrated total, and the remaining part that cannot be divided is called the total remainder. Divide the total remainder by the circumference; if it can be evenly divided by one, it is the star-integrated previous year; if it can be evenly divided by two, it is the total previous year; if it cannot be divided, it is the total year. Subtract the circumference from the total remainder to get the minute fraction. The combination of gold and water, odd numbers are morning, even numbers are evening.
Then, multiply the number of months and the month's remainder separately by the integrated total; if the result can be evenly divided by the total month method, you get the month, and the remaining part that cannot be divided is the month's remainder. Subtract the integrated month from the accumulated month; the remaining is the entry month. Multiply it by the chapter leap; if it can be evenly divided by the chapter month to get a leap, subtract the entry month, and subtract the remaining part in the year; this is called the correct calculation, total month. If it is a leap year, use the moon to control it.
Multiply the common method by the month's remainder, multiply the total month method by the moon's small remainder, then divide by the number of meetings; if the result can be evenly divided by the daily method to get one, it is the star-integrated day of the month. The remaining part is the day's remainder; this is called the outer calculation of the moon. Multiply the circumference by the degree fraction; if it can be evenly divided by the daily method to get one degree, the remaining part is the remainder; this degree is calculated from the five in front of the ox.
The above is the method for calculating the star conjunction (求星合的方法). Finally, add the number of months and their remainders together; if it can be evenly divided by the total month method to get one month, then it is the total year; if it can be evenly divided, subtract it; if it is a leap year, calculate the leap year; the remaining is the later year; if it is full, then it is the next two years. Gold and water add morning to get evening, add evening to get morning.
First, let's talk about the method for calculating the lunar phase and remainder. Add the phase and remainder of the new moon together; if the total exceeds a month, add either twenty-nine days (large remainder) or seven hundred seventy-three parts (small remainder). When the small remainder reaches its maximum, calculate it using the method for large remainders, and the remaining steps follow the same procedure. Next, calculate the entry date and daily remainder. Add the entry date and daily remainder together; if the remainder is sufficient for a full day, add one day. If the small remainder exactly fills the gap from the previous new moon, then subtract one day; if the small remainder exceeds seven hundred seventy-three, subtract twenty-nine days; if it is insufficient, subtract thirty days, and the remaining amount will be calculated using the following method for determining the entry date. Finally, calculate the angles. Add the angles together, including their remainders; if the total is equivalent to a full day's worth of angles, add one angle. Below are the operational data for Jupiter, Mars, Saturn, Venus, and Mercury:
Jupiter: observed for 32 days, 3,484,646 minutes; visible for 366 days; observed running 5 degrees, 2,509,956 minutes; visible running 40 degrees (accounting for retrograde motion of 12 degrees, actual running 28 degrees).
Mars: observed for 143 days, 973,113 minutes; visible for 636 days; observed running 110 degrees, 478,998 minutes; visible running 320 degrees (accounting for retrograde motion of 17 degrees, actual running 303 degrees).
Saturn: observed for 33 days, 166,272 minutes; visible for 345 days; observed running 3 degrees, 1,733,148 minutes; visible running 15 degrees (accounting for retrograde motion of 6 degrees, actual running 9 degrees).
Venus: observed in the east in the morning for 82 days, 113,908 minutes; visible in the west for 246 days (accounting for retrograde motion of 6 degrees, actual running 240 degrees); observed in the east in the morning running 100 degrees, 113,908 minutes; visible in the east (the daily angle is the same as that in the west, observed for 10 days, with 8 degrees of retrograde motion).
Mercury: observed in the east in the morning for 33 days, 612,505 minutes; visible in the west for 32 days (accounting for retrograde motion of 1 degree, actual running 31 degrees); observed running 65 degrees, 612,505 minutes; visible in the east (the daily angle is the same as that in the west, observed for 18 days, with 14 degrees of retrograde motion).
First, let's talk about how to calculate the movement of this celestial body. Start by subtracting the daily movement of the celestial body from that of the sun. If the remaining degrees exactly equal a standard value we calculated earlier (the solar day method), then it means we've calculated correctly, and the celestial body has appeared! Next, multiply the celestial body's movement degrees by a denominator (which is a ratio coefficient we set earlier), and then divide the remaining degrees by the solar day method. If it exceeds half, treat it as fully divided. Then, add the calculated degrees to the sun's daily movement degrees; if the total is an integer, it means the celestial body has moved one degree. The calculation methods differ for direct and retrograde motion, and you need to choose the corresponding denominator based on the direction of motion at that time. During the calculation process, if there are remaining degrees, carry them into the next calculation; subtract them for retrograde motion. If there aren't enough degrees to subtract, use the ratio method, using the degrees of movement as the ratio coefficient for adjustment. Basically, terms like "excess," "approximate," and "full" are all about getting precise division results; while "remove," "and," and "divide" help us get the final precise degree.
Next, let's take a look at the details about this planet (Jupiter). This planet appears in the morning with the sun, then it "hides" (or conceals itself). During its direct motion, it moves 1,742,323 minutes in 16 days, while the planet itself moves for 2,323,467 minutes. Then it appears in the east, behind the sun. During its direct motion, it moves quickly, covering eleven-fifty-eighths of its path each day, completing eleven degrees over 58 days. As it continues its direct motion, it slows down, moving nine minutes each day, covering nine degrees over 58 days. Sometimes it stops and remains stationary for 25 days. During retrograde motion, it moves back one-seventh of a degree each day, covering twelve degrees overall in 84 days. After stopping again for 25 days, it resumes its forward motion, moving nine-fifty-eighths each day and covering nine degrees over 58 days. It speeds up again during direct motion, moving eleven minutes each day and completing eleven degrees in 58 days, appearing in front of the sun and setting in the west in the evening. Sixteen days later, it appears again with the sun, covering 1,742,323 minutes, while the planet itself moves for 2,323,467 minutes. In total, one cycle is 398 days, covering 3,484,646 minutes, while the planet itself moves for 43,250,956 minutes.
In the morning, the sun and Mars align, causing Mars to disappear. Then it starts its direct motion, lasting 71 days, moving 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes. After that, we can see it in the east in the morning, behind the sun. During its direct motion, Mars covers fourteen-thirds of a degree each day, completing 112 degrees in 184 days. Its direct motion speed then slows down, moving twelve-thirds of a degree each day and covering 48 degrees over 92 days. Then it stops and remains stationary for 11 days. It then goes into retrograde, moving back seventeen sixty-thirds of a degree each day and covering 17 degrees in 62 days. It stops again for 11 days, then starts moving forward, moving 12 minutes each day and covering 48 degrees over 92 days. During the next phase of direct motion, it speeds up, moving 14 minutes each day and covering 112 degrees in 184 days, appearing in front of the sun and setting in the west in the evening. After 71 days, moving 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes, it meets the sun again. Throughout one complete cycle, it totals 779 days and 973,113 minutes, covering a total of 414 degrees and 478,998 minutes.
In the morning, the Sun encountered Saturn, and Saturn went into conjunction. Then it began to move forward for 16 days, traveling 1,122,426.5 minutes, equating to 1 degree and 1,995,864.5 minutes. After that, we could see it in the eastern sky in the morning, behind the Sun. While moving forward, Saturn traveled 3/35 of a degree each day, covering 7.5 degrees in 87.5 days. Then it stopped and remained still for 34 days. After another 34 days, it resumed direct motion, moving 3 minutes each day, covering 7.5 degrees in 87 days, at which point it was in front of the Sun, setting in the western sky in the evening. After 16 days, it had traveled 1,122,426.5 minutes, equating to 1 degree and 1,995,864.5 minutes, before meeting the Sun again. Over the entire cycle, it totaled 378 days and 166,272 minutes, covering 12 degrees and 1,733,148 minutes.
As for Venus, when it conjoined with the Sun in the morning, it went into hiding and went retrograde, receding by 4 degrees over 5 days, and then it could be seen in the eastern sky in the morning, behind the Sun. While retrograde, it moved 3/5 of a degree each day, retreating 6 degrees in 10 days. Then it stopped for 8 days. After that, it changed to direct motion, moving slowly at a rate of 3/33 of a degree each day, covering 33 degrees in 46 days to resume direct motion. When moving faster, it traveled 1 degree and 91/15 minutes each day, covering 106 degrees in 91 days. Then it moved forward even faster, traveling 1 degree and 91/22 minutes each day, covering 113 degrees in 91 days, at which point it was behind the Sun, appearing in the eastern sky in the morning. During direct motion, it traveled 1/56,954 of a circle in 41 days, covering 50 degrees plus 1/56,954 of a circle, and then it conjoined with the Sun. The total time for one conjunction was 292 days plus 1/56,954 of a circle, following the same pattern as the planet.
Venus, when it aligns with the sun at night, moves quietly, following its orbit and traces one fifty-fourth of its orbit in forty-one days, tracing fifty degrees and one fifty-fourth of its orbit, then it can be seen in the west in front of the sun at night. It moves swiftly, covering one degree and two twenty-second of a degree per day, and one hundred and thirteen degrees in ninety-one days. Then it slows down, moving at a rate of one fifteenth of a degree per day, and one hundred and sixty degrees over ninety-one days. While moving slowly, it covers thirty-three degrees over forty-six days. Then it comes to a stop for eight days. After that, it starts moving in retrograde, moving three-fifths of a degree each day, receding six degrees over ten days, appearing in the west in front of the sun at night, moving swiftly in retrograde, receding four degrees over five days, and then aligning with the sun once more. The two alignments together span five hundred eighty-four days and one eleventh of an orbit, and the planet follows this pattern.
Mercury, when it aligns with the sun in the morning, moves quietly, receding seven degrees in nine days, then it appears in the east behind the sun in the morning. Continuing its swift retrograde motion, it recedes one degree each day. Then it stops and remains still for two days. After that, it begins its direct motion, moving slowly, tracing eight-ninths of a degree each day, and eight degrees in nine days. When moving quickly, it travels one and a quarter degrees each day, and twenty-five degrees in twenty days, appearing in the east behind the sun in the morning. It moves directly, tracing thirty-two degrees and one sixty-seventh of its orbit in sixteen days, and aligns with the sun once more. The alignment spans fifty-seven days and one sixty-seventh of an orbit, and the planet follows this pattern.
It is said that Mercury, when it sets with the sun, appears to hide. Its orbit is varied, sometimes direct, sometimes retrograde. Specifically, in sixteen days, it can cover 32 degrees and 641,967/1 minutes. In the evening, it can be seen in the western sky at dusk, always in front of the sun.
When moving forward, it moves quickly, covering 1.25 degrees in a day, so in twenty days it covers 25 degrees. When it slows down, it only covers 7/8 degrees in a day, taking nine days to cover just 8 degrees. At times, it even pauses for two days. When retrograde, it moves backwards, retreating 1 degree a day, still in front of the sun, lurking in the west in the evening. Retrograde movement is slow, taking nine days to retreat 7 degrees, eventually reuniting with the sun.
From its conjunction with the sun to the next conjunction, the entire cycle lasts 115 days and 61,255 minutes; that's how Mercury moves. "Mercury: In the evening, it sets with the sun, lurking, direct, sixteen days 641,967/1 minutes, appearing in the west in front of the sun. Direct, swift, covering 1.25 degrees a day, in twenty days covering 25 degrees. Slow, covering 7/8 degrees in a day, taking nine days to cover just 8 degrees. Pause, not moving for two days. Rotate, retrograde, retreating 1 degree a day, in front of the sun, lurking in the west in the evening. Retrograde, slow, taking nine days to retreat 7 degrees, eventually reuniting with the sun. Conjunction, repeating, 115 days and 61,255 minutes; the planet moves in this way."
